Traditionally, heuristics are employed to choose among possible tree paths, ideally producing an optimal sequence of actions resulting from a non-uniform expanded search tree. At first sight such an operation seems impossible to perform quantum mechanically. However, combining Amplitude Amplification [1]} with some performance metric may yield a quantum heuristic that can perform some interesting tricks. It is possible to amplify terms in a general superposition state that respects some threshold value, or even perform pruning. The latter case can be pictured by the rather trivial example of a 2-qubit uniform superposition state. In this case, if one marks a single superposition term then it is known that a single amplitude amplification iteration results in the marked state with certainty [2]}. If instead of measuring the state, one keeps evolving it according to some operator, then it can be interpreted as pruning branches of a tree.
